if one card is drawn from deck of cards, find the probability of getting the following. Enter your answers as fractions or as decimals rounded to 3 decimal places. P (ace or king or jack)

Question

If one card is drawn from an ordinary deck of cards, find the probability of getting the following.

Enter your answers as fractions or as decimals rounded to 3 decimal places.

1. P (ace or king or jack)

Answer 1

Playing cards make for great probability exercises, because they have different ways in which cards can be categorized. Solving these problems relies on you being able to identify and count the number of categories. When solving new types of problems, it can be helpful to start at the end and work backwards. The definition of probability is:

P(Event A) = Number of occurrences of Event A/Total Number of events.

To calculate the probability, we need to count the number in the numerator and denominator. Because we are drawing a single card, we have to consider only the total number of cards in an ordinary deck, which usually excludes jokers and contains 52 cards.

Next, we will count the number of occurrences of Event A. In this case, we have three types of cards connected with the word "or." This means that we have to consider whether events are mutually exclusive. In this case, ask yourself whether you can draw a card and it can be a ace and a king, for example? In this example, were considering different types of cards that are mutually exclusive, and therefore we can add the total number of events together.

Each type of card occurs four times each in an ordinary deck. That is, there are four aces, four kings, and four jacks. This means that we add these numbers together, and the number of occurrences of event A is equal to 12.

We can substitute these numbers into the equation:

P(Event A) = Number of occurrences of Event A/Total Number of events = 12/52 = 0.2308

Rounded to three decimal places, the answer is 0.231.